The Belgium Under-21 striker has also been approached to play for Kenya, after scoring five goals in France this season.
Arsenal are also believed to be interested in the young forward.
Origi is just 18-years-of-age, while both Premier League clubs have sent scouts to watch him in action, ahead of possible summer bids.
Liverpool are planning for life in the Champions League next season, whilst manager Brendan Rodgers is looking to continue the clubs policy of investing in talented young players.
The Liverpool boss is also monitoring Julian Brandt, 17, and Son Heung-Min, 21, both at Bayern Leverkusen.
Meanwhile, Liverpool skipper Steven Gerrard has warned his teammates their 10 game winning streak will mean nothing if the club fails to deliver the Premier League title.
“Every game is getting bigger,” Gerrard said.
“Manchester City was always going to be huge because they are in the race with us but Norwich now become Manchester City.
“Norwich become Chelsea. Norwich become Manchester United. That’s how big it is. We have to treat Norwich City like we treated AC Milan in 2005 (in the Champions League final).
“We can’t think about what colour shirts Norwich are wearing and the personnel in them.
“We have to treat them like the best team in the world. Ten wins in the Premier League is remarkable but you get nothing for it.”
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